An Introduction To

1
An Introduction To Two Port Networks
The University of Tennessee Electrical and
Computer Engineering Knoxville, TN
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2
Two Port Networks
Generalities
The standard configuration of a two port
I1
I2
The Network


Input Port
Output Port
V1
V2
_
_
The network ?
The voltage and current convention ?

notes
3
Two Port Networks
Network Equations
V1 z11I1 z12I2 V2 z21I1 z22I2
V2 b11V1 - b12I1 I2 b21V1 b22I1
Impedance Z parameters
V1 h11I1 h12V2 I2 h21I1 h22V2
I1 y11V1 y12V2 I2 y21V1 y22V2
Admittance Y parameters
Hybrid H parameters
V1 AV2 - BI2 I1 CV2 - DI2
Transmission A, B, C, D parameters
I1 g11V1 g12I2 V2 g21V1 g22I2
notes
4
Two Port Networks
Z parameters
z11 is the impedance seen looking into port 1
when port 2 is open.
z12 is a transfer impedance. It is the ratio of
the voltage at port 1 to the current at port 2
when port 1 is open.
z21 is a transfer impedance. It is the ratio of
the voltage at port 2 to the current at port 1
when port 2 is open.
z22 is the impedance seen looking into port 2
when port 1 is open.
notes
5
Two Port Networks
Y parameters
y11 is the admittance seen looking into port 1
when port 2 is shorted.
y12 is a transfer admittance. It is the ratio of
the current at port 1 to the voltage at port 2
when port 1 is shorted.
y21 is a transfer impedance. It is the ratio of
the current at port 2 to the voltage at port 1
when port 2 is shorted.
y22 is the admittance seen looking into port 2
when port 1 is shorted.
notes
6
Two Port Networks
Z parameters
Example 1
Given the following circuit. Determine the Z
parameters.
Find the Z parameters for the above network.
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Two Port Networks
Z parameters
Example 1 (cont 1)
For z11
For z22

Z11 8 2030 20 ?
Z22 2030 12 ?
For z12
Therefore

?
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Two Port Networks
Z parameters
Example 1 (cont 2)
The Z parameter equations can be expressed
in matrix form as follows.
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Two Port Networks
Z parameters
Example 2 (problem 18.7 Alexander Sadiku)
You are given the following circuit. Find the Z
parameters.
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Two Port Networks
Z parameters
Example 2 (continue p2)
but

Other Answers
Z21 -0.667 ? Z12 0.222 ? Z22 1.111 ?
Substituting gives
or
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Two Port Networks
Transmission parameters (A,B,C,D)
The defining equations are
V2 0
I2 0
V2 0
I2 0
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Two Port Networks
Transmission parameters (A,B,C,D)
Example
Given the network below with assumed voltage
polarities and Current directions compatible with
the A,B,C,D parameters.
We can write the following equations.
V1 (R1 R2)I1 R2I2 V2 R2I1 R2I2
It is not always possible to write 2 equations in
terms of the Vs and Is Of the parameter set.
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Two Port Networks
Transmission parameters (A,B,C,D)
Example (cont.)
V1 (R1 R2)I1 R2I2 V2 R2I1 R2I2
From these equations we can directly evaluate the
A,B,C,D parameters.


I2 0
V2 0


V2 0
I2 0
Later we will see how to interconnect two of
these networks together for a final answer
notes
14
Two Port Networks
Hybrid Parameters
The equations for the hybrid parameters are
V2 0
I1 0
V2 0
I1 0
notes
15
Two Port Networks
Hybrid Parameters
The following is a popular model used to
represent a particular variety of transistors.
We can write the following equations
notes
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Two Port Networks
Hybrid Parameters
We want to evaluate the H parameters from the
above set of equations.
K1

K2

I1 0
V2 0
K3


V2 0
I1 0
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Two Port Networks
Hybrid Parameters
Another example with hybrid parameters.
Given the circuit below.
The equations for the circuit are
V1 (R1 R2)I1 R2I2 V2 R2I1 R2I2
The H parameters are as follows.
1


V20
I10
- 1


V20
I10
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Two Port Networks
Modifying the two port network
Earlier we found the z parameters of the
following network.
notes
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Two Port Networks
Modifying the two port network
We modify the network as shown be adding elements
outside the two ports
We now have
V1 10 - 6I1
V2 - 4I2
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Two Port Networks
Modifying the two port network
We take a look at the original equations and the
equations describing the new port conditions.
V1 10 - 6I1
V2 - 4I2
So we have,
10 6I1 20I1 8I2 -4I2 8I1 12I2
notes
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Two Port Networks
Modifying the two port network
Rearranging the equations gives,
8
26
10
0
16
8
0.4545
-0.2273
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Two Port Networks
Y Parameters and Beyond
Given the following network.

1. Find the Y parameters for the network.
2. From the Y parameters find the z parameters

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Two Port Networks
Y Parameter Example
I1 y11V1 y12V2 I2 y21V1 y22V2
short
We use the above equations to evaluate the
parameters from the network.
To find y11
so
s 0.5

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Two Port Networks
Y Parameter Example
We see
0.5 S
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Two Port Networks
Y Parameter Example
To find y12 and y21 we reverse things and
short V1
short
We have
We have
0.5 S
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Two Port Networks
Y Parameter Example
Summary
Y

Now suppose you want the Z parameters for the
same network.
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Two Port Networks
Going From Y to Z Parameters
For the Y parameters we have
For the Z parameters we have
From above

Therefore
where
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Two Port Parameter Conversions
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Two Port Parameter Conversions
To go from one set of parameters to another,
locate the set of parameters you are in, move
along the vertical until you are in the row that
contains the parameters you want to convert to
then compare element for element
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Interconnection Of Two Port Networks
Three ways that two ports are interconnected
ya
Parallel
yb
za
Series
zb
Cascade
Ta
Tb
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Interconnection Of Two Port Networks
Consider the following network
I1
I2


V1
V2
T1
T2
_
_
Referring to slide 13 we have
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Interconnection Of Two Port Networks
Multiply out the first row
Set I2 0 ( as in the diagram)
Can be verified directly by solving the circuit
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Basic Laws of Circuits
End of Lesson
Two-Port Networks